def is_pell_transformation_ok(eq):
"""
Test whether X*Y, X, or Y terms are present in the equation
after transforming the equation using the transformation returned
by transformation_to_pell(). If they are not present we are good.
Moreover, coefficient of X**2 should be a divisor of coefficient of
Y**2 and the constant term.
"""
A, B = transformation_to_DN(eq)
u = (A * Matrix([X, Y]) + B)[0]
v = (A * Matrix([X, Y]) + B)[1]
simplified = diop_simplify(eq.subs(zip((x, y), (u, v))))
coeff = dict(
[reversed(t.as_independent(*[X, Y])) for t in simplified.args])
for term in [X * Y, X, Y]:
if term in coeff.keys():
return False
for term in [X**2, Y**2, 1]:
if term not in coeff.keys():
coeff[term] = 0
if coeff[X**2] != 0:
return divisible(coeff[Y**2], coeff[X**2]) and \
divisible(coeff[1], coeff[X**2])
return True
def is_pell_transformation_ok(eq):
"""
Test whether X*Y, X, or Y terms are present in the equation
after transforming the equation using the transformation returned
by transformation_to_pell(). If they are not present we are good.
Moreover, coefficient of X**2 should be a divisor of coefficient of
Y**2 and the constant term.
"""
A, B = transformation_to_DN(eq)
u = (A*Matrix([X, Y]) + B)[0]
v = (A*Matrix([X, Y]) + B)[1]
simplified = diop_simplify(eq.subs(zip((x, y), (u, v))))
coeff = dict([reversed(t.as_independent(*[X, Y])) for t in simplified.args])
for term in [X*Y, X, Y]:
if term in coeff.keys():
return False
for term in [X**2, Y**2, 1]:
if term not in coeff.keys():
coeff[term] = 0
if coeff[X**2] != 0:
return divisible(coeff[Y**2], coeff[X**2]) and \
divisible(coeff[1], coeff[X**2])
return True